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DOEbased Automatic Process Control with Consideration of Model Uncertainties

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Process variation is mainly caused by the change of unavoidable noise ... Designed Experiment Result (Engel, 1992) Parameter Estimation Error. 16. RPD Settings ... – PowerPoint PPT presentation

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Title: DOEbased Automatic Process Control with Consideration of Model Uncertainties


1
DOE-based Automatic Process Control with
Consideration of Model Uncertainties
Jan Shi and Jing Zhong The University of
Michigan C. F. Jeff Wu Georgia Institute of
Technology
2
Outline
  • Introduction
  • DOE-based Automatic Process Control with
    Consideration of Model Uncertainty
  • Process model
  • Control objective function
  • Controller design strategies
  • Simulation and case study
  • Summary

3
Problem Statement
  • Process variation is mainly caused by the change
    of unavoidable noise factors.
  • Process variation reduction is critical for
    process quality improvement.
  • Offline Robust Parameter Design (RPD) used at the
    design stage
  • To set an optimal constant level for controllable
    factors that can ensure noise factors have a
    minimal influence on process responses
  • Based on the noise distribution but not requiring
    online observations of noise factors
  • Online Automatic Process Control (APC) during
    production
  • With the increasing usage of in-process sensing
    of noise factors, it will provide an opportunity
    to online adjust control factors to compensate
    the change of noise factors, which is expected
    to achieve a better performance than offline RPD.

4
Motivation of Using APC
y(x,e)
xx1
?b
?a
e
noise distribution
5
The Objective and Focus
The research focuses on the development of
automatic process control (APC) methodologies
based on DOE regression models and real-time
measurement or estimation of noise factors for
complex mfg processes
6
Literature Review
  • For complex discrete manufacturing processes, the
    relationship between the responses (outputs) and
    process variables (inputs) are obtained by DOE
    using a response surface model, rather than using
    dynamic differential/difference equations
  • offline robust parameter design (RPD) (Taguchi,
    1986)
  • Improve robust parameter design based on the
    exact level of the observed uncontrollable noise
    factors (Pledger,1996)
  • Existing APC literature are mainly for automatic
    control of dynamic systems that are described by
    dynamic differential/difference equations.
  • Certainty Equivalence Control (CEC) (Stengel,
    1986) The controller design and state estimator
    design are conducted separately (The uncertainty
    of system states is not considered in the
    controller design)
  • Cautious Control (CC) (Astrom and Wittenmark,
    1995) The controller is designed by considering
    the system state estimation uncertainty, which is
    extremely difficult for a complex nonlinear
    dynamic system.
  • Jin and Ding (2005) proposed Doe-Based APC
    concepts
  • considering on-line control with estimation of
    some noise factors.
  • No interaction terms between noise and control
    factors in their model.

7
Objective
  • Develop a general methodology for controller
    design based on a regression model with
    interaction terms.
  • Investigate a new control law considering model
    parameter estimation uncertainties
  • Compare the performances of CC, CEC, and RPD, as
    well as performance with sensing uncertainties.

8
Methodology Development Procedures ? APC Using
Regression Response Models
Obtain significant factors estimated process
model
S1 Conduct DOE and process modeling
Based on key process variable



S2 Determine APC control strategy (considering
model errors
Use certainty equivalence control or cautious
control
Based on observation uncertainty


Based on process operation constraints on
controller
S3 Online adjust controllable factors

Obtain reduced process variation


S4 Control performance evaluation


9
1. Process Variable Characterization
Process Variables
Noise Factors
Controllable Factors
Off-line setting Factors
Unobservable Noise Factors
On-line adjustable Factors
Observable Noise Factors
Y f (X, U, e, n)
10
2. Control System Framework
Observable Noise Factors (e)
Unobservable Noise Factors (n)
Noise Factors
Target
Feedforward Controller
Manufacturing Process
Response (y)
Controllable Factors (x)
Predicted Response
In-Process Sensing of e
Observer for Noise Factors (e)
11
3 Controller Design3.1 Problem Assumptions
  • The manufacturing process is static with smoothly
    changing variables over time Parameter Stability
  • e, n and e are independent, with E(e)0,
    Cov(e)Se, E(n)0, Cov(n)Sn, E(e)0, Cov(e)Se.
    e are i.i.d.
  • Estimated process parameters denoted by
    ,
  • is estimated from
    experimental data.
  • Observations of measurable noise factors, denoted
    by , are unbiased, i.e.,
    and .

12
3 Controller Design 3.2 Objective Function
Objective Function (Quadratic Loss)
Optimization Problem
13
3 Controller Design 3.3 Control Strategy
Procedure for Solving Optimization Problem
Step 2 obtain X by solving optimization problem
of JAPC
Process Control Strategy Two Step Procedure
Step 1 Off-line Controllable Factors Setting
Step 2 On-line Automatic Control Law
14
4. Case Study An Injection Molding Process
Process Description
Response Variable (y) Percentage
Shrinkage of Molded Parts
Process Variables
15
DOE Modeling
Designed Experiment Result (Engel, 1992)
Reduced DOE Model after Coefficient Significance
Tests
Parameter Estimation Error
16
Robust Parameter Design
Response Model
Variance Model
RPD Settings
u1 and x3 are adjusted according to target values
as in right table
17
DOE-Based APC
Objective Loss Function
Optimal Settings
where
18
Simulation Results
Comparison of RPD, CE control and Cautious Control
Assuming
Optimal Off-line Setting
Cautious control law performs much better than RPD
Control Strategy Evaluation
19
Simulation Results - 2
Certainty Equivalence assume observation perfect
CE controller performs much better than RD when
the measurement is perfect, but its advantage
decreases when the measurement is not perfect,
and will cause a larger quality loss than RPD
controller under high measurement uncertainty.
20
Control strategy with partial sensing failure 1
  • Sensor noise level change no modeling error

150 observations, sensor noise level increased
from point 51 to 100, then restored. t1.6
CE Control suffers greatly from noise level change
Mean of RPD has deviated from target
21
Control strategy with partial sensing failure 2
  • Sensor noise level change

APC considering modeling error
255 observations, sensor noise level increased
from point 101 to 200, then restored
Overall J/J_ce16.8. APC performance is steady
over different noise levels.
22
Control strategy with partial sensing failure 3
  • Sensor failure

- Assume no modeling error, - 250 observations,
sensor failed from point 51 to 150, then repaired
Control Strategy
Switch to RPD setting after the detection of
sensor failure - Actual system will have step
response
23
Industrial Collaboration with OG Technologies
DOE-Based APC Test bed in Hot Deformation
Processes
24
Summary
  • DOE-Based APC performs better than RPD when
    measurable noise factors are present with not too
    large measurement uncertainty.
  • RPD should be employed in case of too large
    measurement uncertainty or there are no
    observable noise factors.
  • Cautious control considering measurable noise
    factors and model estimation uncertainty performs
    better than RPD and CE strategy.
  • Model updating and adaptive control with
    supervision are promising or the future study.

25
Impacts
  • Expanding the DOE from off-line design and
    analysis to on-line APC applications, and
    investigates the associated issues in the DOE
    test design and analysis
  • Developing a new theory and strategy to achieve
    APC by using DOE-based models including on-line
    DOE model updating, cautious control, and
    supervision.
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